Lamentable Lagrange articles.

[HopDavid]

Lamentable Lagrange Articles

The Lagrange points are one of my interests. I am a little obsessed with the Earth Moon Lagrange 2 point.

One of my pet peeves are wrong explanations of these five locations. So many articles and Youtube videos claim these are locations where gravitational forces cancel each other out.

One of many examples is Fraser Cain's video What Are The Lagrange Points? Finding Stable Points In Space. From that video: 

Quote

"There are places in the Solar System where the forces of gravity balance out perfectly. Places we can use to position satellites, space telescopes and even colonies to establish our exploration of the Solar System. These are the Lagrange Points."

People often sensibly ask about L2 and L3. At both these locations the central and orbiting body both pull the same direction.  How do those cancel each other? Or at the L4 and L5 where the gravity vectors are 60º from each each other.  

The only place where the two massive bodies pull in opposite directions is L1. And even at that location gravity does not cancel out. 

At the Sun Earth L1 point the sun's pull is about 34 times that of earth's. So, nope, the opposing gravities do not cancel at that location.

At the Earth Moon L1 the earths pull is about 2.6 times that of the Moon's. So, nope, gravity doesn't cancel out there either.

It's a three man tug of war. Enter Voldemort.

There are three men in this tug of war.

At the Earth Moon L2 the Earth and Moon are pulling the same direction against a third man who, like Voldemort, shall not be named. 

At the Sun Earth L1 point the earth is helped by Voldemort who at that location in nearly as strong as the sun's gravity.

At L4 and L5 Voldemort is pulling nearly opposite the central body's tug. But not directly away from the center of the central body. Rather away from the barycenter of the two massive bodies. So Voldemort exactly cancels the central body's gravity and the small sideways tug of the orbiting body. I've attached an illustration of the Pluto Charon system. Pluto and Pluto's gravity is purple. Charon and Charon's gravity I've colored orange. And Voldemort is colored blue.

Voldemort is Centrifugal Force

The unnamed contestant in this three man tug of war is Centrifugal Force. Just about everyone is familiar with centrifugal force. It's what you feel on a spinning carnival ride. Or in a car making a turn.

Why do high school physics teachers refuse to mention centrifugal force? Is it a ruthless entity set on world domination?

No. It is avoided because "centrifugal force" or "centrifugal acceleration" are misnomers. It is not truly an acceleration. Rather it is just inertia, the tendency to travel in a straight line. However in a rotating frame inertia feels like a force.

And, indeed, it can be treated like an acceleration if you're in a rotating frame.

The pseudo acceleration can be expressed as ω² r. Where ω is angular velocity in radians over time.

Clueless Pedantry.

It is a good thing to distinguish between inertia and acceleration. In my opinion it is sufficient to preface the term with "pseudo" or "so called" and proceed to use this pseudo force or acceleration when examining rotating systems. It is commonly used by engineers and even physicists. Coriolis force is also commonly used even though it is not truly a force.

Dealing with this by eliminating it from our lexicon will lead to confusion. As illustrated by the many Lagrange explainers that are completely incorrect.

 

 

 

 

Edited Wednesday at 08:40 PM by HopDavid
Fixed some typos

[Mordred]

First off inertia is constant velocity which is a vector (magnitude and direction) when you change directions it is acceleration not pseudo inertia. You need to include all three laws of inertia when defining inertia it's not just the tendency to travel in straight lines it also includes the constancy of speed as well as direction.

Acceleration involves both change in velocity and change in direction.

Secondly from what I read  above this seems to belong under our Speculation forum and not the lounge.  I will let one of the mods determine if  it meets the requirements under one of the mainstream physics forums.

Edited Wednesday at 10:10 PM by Mordred

[studiot]

Since you have transferred centrifugal force discussion from the Tyson thread to here, but not replied to my comments there,

are you aware that D'Alembert's solution is a direct consequence of the Theorem of Virtual Work, which in turn can be deduced from Poinsot's theorem?

Both have extensive use in Mechanics and other fields.

[Mordred]

8 minutes ago, studiot said:

 Poinsot's theorem?

 

Now there's a theorem I haven't heard mentioned in ages lol. I almost completely forgot about that theorem.

[swansont]

2 hours ago, HopDavid said:

Why do high school physics teachers refuse to mention centrifugal force?

Probably because teaching Newton’s laws of motion is difficult enough, and there’s no immediate need to solve problems in a non-inertial frame

2 hours ago, HopDavid said:

Is it a ruthless entity set on world domination?

No. It is avoided because "centrifugal force" or "centrifugal acceleration" are misnomers. It is not truly an acceleration. Rather it is just inertia, the tendency to travel in a straight line. However in a rotating frame inertia feels like a force.

No, it’s a force, but it’s a pseudoforce, which you need to introduce in order to use F=ma in an accelerating frame. Newton’s first law tells you the laws of motion don’t apply, but by pretending you are moving in uniform motion you can use them. 

Quote

One of many examples is Fraser Cain's video

Except that, from your quote, he doesn’t say they cancel, he says they balance. L1 is an orbit, so must be a force there. A centripetal force, if analyzing in an inertial frame. But you want the period to be the same as the earth’s. The earth’s gravity cancels out the excess gravity of the sun, so the net force (centripetal force) is correct for that orbit. That’s the balance you achieve. 

There’s more than one way to explain this, and more than one way to understand it. Your tone suggests that not doing it your preferred way is wrong, and that’s simply not the case. They could be, but everyone is from time to time. But Frasier Cain, Cox, NdGT, et al, are out there, engaging with the public, and not hiding behind pseudonyms to take potshots

You want to discuss science? Great! You can do it without bashing people. 

[Mordred]

19 minutes ago, swansont said:

Probably because teaching Newton’s laws of motion is difficult enough, and there’s no immediate need to solve problems in a non-inertial frame

That is a key distinction between centripetal and centrifugal force. I was about to mention that but you beat me to it.

[HopDavid]

1 hour ago, Mordred said:

First off inertia is constant velocity which is a vector (magnitude and direction) when you change directions it is acceleration not pseudo inertia. You need to include all three laws of inertia when defining inertia it's not just the tendency to travel in straight lines it also includes the constancy of speed as well as direction.

Acceleration involves both change in velocity and change in direction.

Secondly from what I read  above this seems to belong under our Speculation forum and not the lounge.  I will let one of the mods determine if  it meets the requirements under one of the mainstream physics forums.

First off nothing you've said refutes anything I wrote.

Secondly this isn't speculation. Rather it is freshman physics.

Thirdly The Lounge description says "Discuss life, work, school, anything!"  However it seems somebody transferred this to a different forum. I'm okay with classical physics.

[Mordred]

Ok believe what you like. Doesn't change my reply if your going to lecture others you might want to use correct terminology. Particularly when it comes to properly understanding the difference between inertia and acceleration.

It is after all clearly defined in any classical textbook.

For that matter most classical textbooks don't bother explaining centrifugal force for the reasons Swansont mentioned above.

Let's start with the statement Valdemort is centrifugal force.

Now ask yourself under Newtons laws of inertia which direction is a force applied to cause an acceleration let's start there.

PS you might also take last question and ask does that describe a fictitious force ?

Might help you make the connection between inertial vs non inertial observers doing the measurement.

Edited yesterday at 12:17 AM by Mordred

[HopDavid]

1 hour ago, studiot said:

Since you have transferred centrifugal force discussion from the Tyson thread to here, but not replied to my comments there,

are you aware that D'Alembert's solution is a direct consequence of the Theorem of Virtual Work, which in turn can be deduced from Poinsot's theorem?

In the other thread you said d'Alembert introduced m ω² r.

Huygens derived his expression for centrifugal force in 1673. Lambert was born 1717.

I didn't check it out further after that. In any case that thread was about Tyson. 

 

[Mordred]

Have you applied vectors to 

\[f=\frac{mv^2}{r}\] 

Yet in terms of my last post ? Or are you still looking into the distinctions of why that equation does not describe a fictitious force as opposed to

\[f=m\omega^2 r\] 

If it helps use the 1/r^2 relation to gravity.

Via

\[f=\frac{Gm_1m_2}{r^2}\]

Then look at your Langrene example above

1 hour ago, HopDavid said:

 

Secondly this isn't speculation. Rather it is freshman physics.

If your claiming mainstream physics is wrong then it does belong in Speculation.

If it's simply not understanding the distinction then it belongs in mainstream.

Edited yesterday at 12:59 AM by Mordred

[HopDavid]

1 hour ago, swansont said:

Probably because teaching Newton’s laws of motion is difficult enough, and there’s no immediate need to solve problems in a non-inertial frame

No, it’s a force, but it’s a pseudoforce, which you need to introduce in order to use F=ma in an accelerating frame. Newton’s first law tells you the laws of motion don’t apply, but by pretending you are moving in uniform motion you can use them. 

Except that, from your quote, he doesn’t say they cancel, he says they balance. L1 is an orbit, so must be a force there. A centripetal force, if analyzing in an inertial frame. But you want the period to be the same as the earth’s. The earth’s gravity cancels out the excess gravity of the sun, so the net force (centripetal force) is correct for that orbit. That’s the balance you achieve. 

There’s more than one way to explain this, and more than one way to understand it. Your tone suggests that not doing it your preferred way is wrong, and that’s simply not the case. They could be, but everyone is from time to time. But Frasier Cain, Cox, NdGT, et al, are out there, engaging with the public, and not hiding behind pseudonyms to take potshots

You want to discuss science? Great! You can do it without bashing people. 

If you Google Hop David you can find me. I also go by Hollister David. I am not hiding behind a pseudonym.

None of the incorrect Lagrange explainers I've seen make mention of centripetal force force or excess gravity.  Can you show me equations precisely calculating "excess gravity"?

In the attached diagram the center of the Pluto Charon system is the barycenter. Centripetal force is force pointing towards the center. Which of the three vectors I show would you call centripetal? None of them point towards the center of the system.

The magnitude of all three vectors I can figure precisely.

How would you redraw this diagram for your students?

 

[Mordred]

The centripetal force will point towards the barycenter. Which is the effective center of mass.  Both Pluto and Charon will orbit the Barycenter. However you have no mass term for Voldemort so I assume the mass tetm at Valdemorts location is insignificant.

The outward force (fictitious force felt by Valdemort ) in his non inertial frame is the Centrrifugal force.

 

Edited yesterday at 01:34 AM by Mordred

[swansont]

41 minutes ago, HopDavid said:

In the attached diagram the center of the Pluto Charon system is the barycenter. Centripetal force is force pointing towards the center. Which of the three vectors I show would you call centripetal? None of them point towards the center of the system.

You apparently didn’t read my post carefully enough to notice I wrote L1

[Mordred]

@HopDavid would you like you the full system set of equations for the above.

https://jfuchs.hotell.kau.se/kurs/amek/prst/15_lapo.pdf

Your system albeit without names is directly applied in that article.

Edited yesterday at 02:02 AM by Mordred

[HopDavid]

1 hour ago, Mordred said:

If your claiming mainstream physics is wrong then it does belong in Speculation.

Because I use the term "centrifugal force"?

So are you saying Randall Monroe is a crank? (see attached image).

You are presumptuous to appoint yourself the voice of main stream science. 

Plenty of engineers and scientists use it while acknowledging it's a fictitious force. It's very convenient in many scenarios.

[Mordred]

39 minutes ago, HopDavid said:

Because I use the term "centrifugal force"?

So are you saying Randall Monroe is a crank? (see attached image).

You are presumptuous to appoint yourself the voice of main stream science. 

Plenty of engineers and scientists use it while acknowledging it's a fictitious force. It's very convenient in many scenarios.

You really seem to have a reading comprehension  problem or you like to imply what isn't intended.

The lounge is not a place to discuss a physics topic  I described the distinction of what belongs in mainstream physics as opposed to Speculation. I did not imply your thread automatically belonged in Soeculation hence why I let one of the full mods make that determination. 

Had I felt it belonged in Speculation I could have moved it there myself as Resident experts do in fact have that ability.

!

Moderator Note

This is just to demonstrate Resident experts do have some moderation abilities.

Just so we're 100 percent clear on that 

 

The point being Resident experts are members of the moderation team. Pointing out more appropriate forums is part of my duties.

When it comes to that it is a Resident experts primary duty.

Edited yesterday at 03:15 AM by Mordred

[HopDavid]

12 hours ago, swansont said:

You apparently didn’t read my post carefully enough to notice I wrote L1

Okay, for the moment let's pretend L4 and L5 don't exist and let's focus on L1.

Have you ever calculated L1 distances? I have. See my spreadsheet of L1 and L2 points for various bodies in our solar system: Link

I used equations from Szebehely's "Theory of Orbits - The Restricted 3 Body Problem". How did Szebehely get his equations? He considered three vectors: gravity of central body, gravity of orbiting body and centrifugal force. He talks about centrifugal force on pages 8, 38, 629-633 of that book.

Have you heard of Jerrold Marsden? Check out section 8.6 of his Introduction to Mechanics and Symmetry.

Or Shane Ross? From his explainer of how to calculate the collinear Lagrange points: "The effective potential energy (also called the augmented potential) is a way to include both the effects of gravity and the centrifugal force of the rotating frame. The critical points of the effective potential energy function, Ū(x,y,z), are the Lagrange points, equilibrium points in the rotating frame (a.k.a., relative equilibria)."

Marsden, Ross, Lo and Koon enjoyed some notoriety for their Interplanetary Transport Network ideas. Check out page 36 of their online textbook Dynamical Systems, the Three-Body Problem and Space Mission Design.

TL;DR Plenty of bonafide mathematicians and engineers are quite comfortable using the term "centrifugal force". Your attempt at a gotcha is actually an embarrassing tempest in a teapot.

Attached is my illustration of the Pluto Charon L1. Please elaborate on your "excess gravity" concept. How would you redraw this  without using the vector that will not be named?

 

[Mordred]

Why do I get the feeling this is more an attempt to bash others rather than discuss which is a preferable application ?

The choice of which to apply depends on which observer so what is the issue here ?

[HopDavid]

15 hours ago, Mordred said:

@HopDavid would you like you the full system set of equations for the above.

https://jfuchs.hotell.kau.se/kurs/amek/prst/15_lapo.pdf

Your system albeit without names is directly applied in that article.

A nice paper, thank you. As with most papers I've seen looking at Lagrange points they consider the centrifugal force along with the gravities of the central and orbiting bodies. Screen capture of one of the paragraphs attached. 

They also look at Coriolis force (another pseudo force which is actually inertia in a rotating frame). I might try to look at that. I've heard that Coriolis force helps keep L4 and L5 stable. But I've never grokked the notion.

[Mordred]

Your welcome if your familiar with latex and using latex for your math expressions use \[ latex\*] for seperate line and \(latex\*) for inline just remove the * from the last bracket as I put them there to prevent activation.

I figured you might like the paper as your example has excellent similarity to the example within the paper.

 

Edited 17 hours ago by Mordred